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# Tip #10 to Get a Top ACT Math Score

By Brian Leaf
McGraw-Hill Professional

Here are three more math vocab terms. Memorize them, practice using them, and remember to underline them in questions. That will avoid heaps of careless errors.

Factors—Numbers that divide into a number evenly (i.e., without a remainder). Example: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

When asked for the factors of a number, make a list of pairs like the one shown above. This eliminates the possibility of missing any.

Greatest common factor—The largest factor shared by several given numbers. Example: The greatest common factor of 48 and 32 is 16. The number 16 is the largest number that is a factor of both 48 and 32.

Prime factors—The factors of a number that are also prime numbers. (Remember, a prime number is a number whose only factors are 1 and itself.)

Example: The prime factors of 48 are 2 and 3. These are the factors of 48 that also happen to be prime numbers.

Let's look at this question:

Solution: To complete this question, we factor 120 just as we factored 48 above.

Then we circle any prime numbers in the list. The numbers 2, 3, and 5 are the only prime numbers in the list, so there are 3 prime factors.

### Easy

1. Which of the following lists the factors of 60 ?
1. 1, 10, 20, 30, and 60
2. 2, 4, 6, 10, 12, 20, 30, and 60
3. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
4. 1, 2, 3, 4, 5, 6, and 10
5. 60, 120, 180, and 240
2. Which of the following is an odd number that is a factor of 140 ?
1. 2
2. 13
3. 35
1. 37
2. 51
3. ### Medium

4. How many prime integer factors does the number 50 have?
1. None
2. 1
3. 2
4. 6
5. 10
5. ### Hard

6. If a and b are positive integers greater than 1, such that the greatest common factor of a3b and a2b2 is 36, then which of the following could a equal?
1. 36
2. 18
3. 9
1. 6
2. 3
7. If a, b, and c are different odd prime numbers, how many factors does 2abc have?
1. 4
2. 5
3. 15
4. 16
5. 24

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